Current quantitative polymerase chain reaction (PCR) protocols are only indicative of the quantity of a target sequence relative to a standard, because no means of estimating the amplification rate is yet available. The variability of PCR performed on isolated cells has already been reported by several authors, but it could not be extensively studied, because of lack of a system for doing kinetic data acquisition and of statistical methods suitable for analyzing this type of data. We used the branching process theory to simulate and analyze quantitative kinetic PCR data. We computed the probability distribution of the offspring of a single molecule. We demonstrated that the rate of amplication has a severe influence on the shape of this distribution. For high values of the amplification rate, the distribution has several maxima of probability. A single amplification trajectory is used to estimate the initial copy number of the target sequence as well as its confidence interval, provided that the amplification is done over more than 20 cycles. The consequence of possible molecular fluctuations in the early stage of amplification is that small copy numbers result in relatively larger intervals than large initial copy numbers. The confidence interval amplitude is the theoretical uncertainty of measurements using quantitative PCR. We expect these results to be applicable to the data produced by the next generation of thermocyclers for quantitative applications.